On the trellis representation of the Delsarte-Goethals codes

作     者：Shany, Y Reuven, I Be'ery, Y 

作者机构：Tel Aviv Univ Dept Elect Syst Engn IL-69978 Ramat Aviv Israel 

出 版 物：《IEEE TRANSACTIONS ON INFORMATION THEORY》 (IEEE Trans. Inf. Theory)

年 卷 期：1998年第44卷第4期

页      面：1547-1554页

核心收录：

学科分类：0808[工学-电气工程] 08[工学] 0701[理学-数学] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

主　　题：biproper trellis Delsarte-Goethals code Kerdock code rectangular codes trellis complexity 

摘      要：In this correspondence, the trellis representation of the Kerdock and Delsarte-Goethals codes is addressed. It is shown that the states of a trellis representation of DG(m, delta) under any bit-order are either strict-sense nonmerging or strict-sense nonexpanding, except, maybe, at indices within the code s distance set. For delta greater than or equal to 3 and for m greater than or equal to 6, the slate complexity, s(max) [DG(m, delta)], is found. For all values of m and delta, a formula for the number of states and branches of the biproper trellis diagram of DG(m, delta) is given for some of the indices, and upper and lower bounds are given for the remaining indices. The formula and the bounds refer to the Delsarte-Goethals codes when arranged in the standard bit-order.